Communication: Estimating the initial biasing potential for λ-local-elevation umbrella-sampling (λ-LEUS) simulations via slow growth

Abstract

In a recent article [Bieler et al., J. Chem. Theory Comput. 10, 3006-3022 (2014)], we introduced a combination of the λ-dynamics (λD) approach for calculating alchemical free-energy differences and of the local-elevation umbrella-sampling (LEUS) memory-based biasing method to enhance the sampling along the alchemical coordinate. The combined scheme, referred to as λ-LEUS, was applied to the perturbation of hydroquinone to benzene in water as a test system, and found to represent an improvement over thermodynamic integration (TI) in terms of sampling efficiency at equivalent accuracy. However, the preoptimization of the biasing potential required in the λ-LEUS method requires "filling up" all the basins in the potential of mean force. This introduces a non-productive pre-sampling time that is system-dependent, and generally exceeds the corresponding equilibration time in a TI calculation. In this letter, a remedy is proposed to this problem, termed the slow growth memory guessing (SGMG) approach. Instead of initializing the biasing potential to zero at the start of the preoptimization, an approximate potential of mean force is estimated from a short slow growth calculation, and its negative used to construct the initial memory. Considering the same test system as in the preceding article, it is shown that of the application of SGMG in λ-LEUS permits to reduce the preoptimization time by about a factor of four. © 2014 AIP Publishing LLC.

Orthogonal sampling in free-energy calculations of residue mutations in a tripeptide: TI versusλ-LEUS

“…Another interesting aspect of this specific calculation is the observation that salt‐bridge formation is enhanced at an intermediate λ ‐value compared to its occurrence in the KEK end state. We encountered a similar situation in another study concerned with cation binding to crown ethers, where the mutation between two cations with high binding affinities involved intermediate states where the ion‐solvent interactions were strongly enhanced, leading to their escape from the complex, and rendering the orthogonal sampling essentially impossible in the absence of binding restraints. In both cases, these effects are most likely due to an interaction imbalance related to the soft‐core nature of a set of atoms in the intermediate state, rendering specific electrostatic interactions closer‐ranged and thus extremely favorable.…”

“…The θ variable was assigned a mass parameter m θ = 75 u nm 2 (where ) and was separately thermostated at 300 K using a Nosé–Hoover chain (NHC) of 10 variables, all with a coupling time τ NHC = 0.1 ps. The memory was initialized using a slow‐growth sweep of 220 ps. This was followed by a LE phase of 2 ns (3 ns for the KEK→KG E K mutation) and an US phase of 20 ns.…”

“…The multiple equilibration periods necessary in TI or HR (one per λ ‐point) can be reduced to a single one, although at the cost of introducing an initial (nonproductive) LE phase. However, the duration of this phase can be significantly reduced by using a short preliminary slow‐growth scan to initialize the memory . Most importantly, compared to TI, λ ‐LEUS is expected to afford a similar sampling advantage as HR in terms of opening up λ ‐dependent pathways that circumvent barriers in the orthogonal DOFs.…”

Vase‐Kite Equilibrium of Resorcin[4]arene Cavitands Investigated Using Molecular Dynamics Simulations with Ball‐and‐Stick Local Elevation Umbrella Sampling

“…Steps e-g are the same as in the LEUS method [99] [106] (see also the related fragment-based, [100] alchemical, [107][108][109][110] and conveyor-belt [77][111] [112] variants). Steps a -d introduce the main features of the B&S approach, namely [101][102] a minimal irrelevant volume open to sampling, the use of one-dimensional memory grids, and a problem-adapted geometry.…”

Multidimensional virtual‐system coupled canonical molecular dynamics to compute free‐energy landscapes of peptide multimer assembly

“…An alternative class of generalized‐ensemble methods including umbrella sampling, adaptive umbrella sampling (AUS), and their variants introduces a structural parameter, for example, intermolecular distance, for the reaction coordinate. In theory, AUS can avoid the oversight described above when major and minor basins can be discriminated on the reaction‐coordinate axis.…”